Do you think that the surface area of your compost pile will provide enough space to grow enough greens to be worthwhile?

To augment your cover crop, might you consider buying some 'greens' like blood meal,urea, or other nitrogen-rich feed/grain? I take it that you don't have access to horse/steer manure supply? You might consider the inexpensive bags of steer manure at nursery.

As to a choice of green manure plant .... I wonder how cheap beans from the grocery story would do? I got quite a thick stand of plants in out of the way part of my garden, where I threw away some weevily navy beans.

I would agree with borderbarb that there's probably not enough surface area to grow a lot of green manure but it's sounds like something I might try for the heck of it. Right now I have sunflowers and sweet peas growing out of compost covered hay bales. To what end I'm not entirely sure but they should look cool if they take off.

I think if you want to grow your greens for your pile you're probably better off setting aside a section of your garden for it. Comfrey is supposed to be excellent for that but it is invasive. I have enough invasive plants growing already so I've kept away from comfrey. I'm growing some borage this year and that is supposedly a good green for the compost pile.

Are you sure you can't scrounge up some greens? A quick search of Cleveland's craiglist showed a handful of people getting rid of hay which is usually a pretty good green in the compost pile. It helps having a pickup truck to get those sort of things.

To get the seeds to germinate your compost pile, at least the top few inches, would need to be wetter then would be good for the aerobic bacteria that are working on digesting the material you put in there. That would, at best, slow the digestion process down possibly even enough so that additional green manure would not do much to help.
Grow the green manure someplace else, cut it, and then add it to your compsot pile.

Ask your neighbors. I have two neighbors who dump their veggie scraps and UCGs into one of my piles.

Wow, interesting responses! Plenty of food for thought, and perhaps for the compost pile too. ;-)

I have a big comfrey plant in my yard that I wouldn't mind getting rid of. It has already flowered though. If I cut it and toss it in the pile, will it go to seed? What if I just toss the leaves and leave the flowers out?

Is hay a green? I thought it was a brown. Straw is a brown, right?

I do need to find a good source of horse manure. I got a little from our police horse stable, but it was mixed with a ton of wood chip bedding which took forever to break down.

Trouble is, you'll be consuming the nutrients in your compost to grow the cover crop (green manure). You might be better off growing a legume or legume-grain mix on uncomposted soil (the legumes will fix nitrogen from the air), then cutting them down when they flower and turning them into your compost and/or the soil they're growing on.

Hay, a food crop for ruminants, is a Green because of the, usually, high protein. Straw, because it is harvested only after the stalks loose almost all the protein they had while growing and producing the seeds (grain) we use is a Brown.
The C:N ratio tells you of many plants that have close to the optimal 30:1 C:N ratio needed to get a compost pile to be digested by the bacteria. If the material going in to your compost pile is relatively fresh vegetative material, is of relatively small particle size, has enough bit no too much moisture, and is able to get sufficient air (very easy in piles smaller then 6 x 6), and is of sufficient volume it will compost with no problem.